Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} V]
  [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : CategoryTheory.MonoidalCategory V]
  {F G : CategoryTheory.Functor C V} [inst_4 : CategoryTheory.MonoidalCategory.DayConvolution F G]
  {F' G' : CategoryTheory.Functor C V} [inst_5 : CategoryTheory.MonoidalCategory.DayConvolution F' G'] (f : F ⟶ F')
  (g : G ⟶ G') (x y : C) {Z : V}
  (h :
    (CategoryTheory.MonoidalCategory.DayConvolution.convolution F' G').obj
        (CategoryTheory.MonoidalCategoryStruct.tensorObj x y) ⟶
      Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.MonoidalCategory.DayConvolution.unit F G).app (x, y))
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.MonoidalCategory.DayConvolution.map f g).app
          (CategoryTheory.MonoidalCategoryStruct.tensorObj x y))
        h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom (f.app x) (g.app y))
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.MonoidalCategory.DayConvolution.unit F' G').app (x, y)) h)

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

12 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.DayConvolutionCategoryTheory.MonoidalCategory.DayConvolution